How do you solve this quadratic equation by completing the square?: x^2 +11x+24=0

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baxthum8 | High School Teacher | (Level 3) Associate Educator

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To complete the square of the quadratic equation:  `x^2 +11x + 24 = 0,`

first, subtract 24 from each side to get:

`x^2 - 11x = -24.`

Then we need to find the value of "c" below that would make the left side of the quadratic a perfect square and also add to the right side to keep equivalent.

`x^2 + 11x + c = -24 + c`

To find "c", divide 11 (b in equation written in standard form) by 2 then square,

so `c = (11/2)^2= 121/4`

Next we have:  `x^2 + 11x + 121/4 = -24 + 121/4`

` `

Since we created a "perfect square" we'll factor to get:

`(x + 11/2)^2 = 25/4`

Now take square root of each side to solve for x, we have:

`x + 11/2 =+- 5/2`

Subtract `11/2`

Therefore `x =+-5/2 - 11/2`

`x = 5/2 - 11/2 = -6/2 = -3`

`x = -5/2 - 11/2 = -16/2 = -8`

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